By: Hesham Hamed Ahmed Ibrahim
A Thesis Submitted in Partial Fulfillment of the
Requirements for the Degree of
DOCTOR OF PHILOSOPHY in
AEROSPACE ENGINEERING
Abstract
Shape memory alloys (SMAs) refer to a group of materials that have a
unique ability to recover large pre-strains completely when heated above
certain characteristic temperature called the austenite finish temperature.
During the strain recovery process, a large tensile recovery stress occurs
if the SMA is restrained.
In this work, a traditional composite plate impregnated with pre-strained
shape memory alloy fibers and subject to the combined effect of thermal,
aerodynamic, and acoustic loads, is investigated to demonstrate the
effectiveness of using the SMA fiber embeddings in improving the static and
dynamic response of composite plates. The problems investigated are: thermal
buckling, aerothermal buckling, linear flutter at elevated temperatures,
flutter nonlinear limit-cycle and chaotic oscillations at elevated
temperatures, nonlinear random vibration under thermal effect, and nonlinear
flutter-random vibration at elevated temperatures.
A new nonlinear finite element model, based on the first-order shear
deformable plate theory, is derived. von Karman strain displacement
relations are utilized to account for geometric nonlinearity. The
aerodynamic pressure is modeled using the quasi-steady first-order piston
theory, while the random acoustic pressure is modeled using a white-Gaussian
acoustic wave. The governing equations are obtained using the principle of
virtual work. The nonlinear temperature dependence of material properties
for the composite matrix and SMA fibers is considered in the formulation.
Newton-Raphson iteration is employed to obtain the static aero-thermal large
deflection at each temperature step and the dynamic response at each time
step of the Newmark numerical integration scheme. An eigenvalue problem is
solved at each temperature step to predict the natural frequencies of the
thermally buckled plate.
A frequency domain solution is presented for predicting the flutter
boundary at elevated temperatures, and an updated eigen-solution procedure
is adopted to obtain the harmonic limit-cycle oscillation amplitude at a
given dynamic pressure and temperature rise. The time domain method is
applied to numerically investigate periodic, non-periodic, and chaotic
limit-cycle oscillations. The finite element modal formulation and solution
procedures are developed for the time domain method. The nonlinear random
response of a shape memory alloy hybrid composite plate subject to the
combined action of thermal, aerodynamic and acoustic excitation is
numerically investigated using procedures developed in flutter section.
The results show that the critical buckling temperature of the plate is
greatly increased and thus the thermal postbuckling deflection is suppressed
by using SMA fiber embeddings. The shape memory alloy hybrid composite
plates display an increase of critical dynamic pressure, enlargement of
statically and dynamically stable region, and decrease of the other regions,
i.e. buckled, limit-cycle oscillation and chaotic regions. Compared with
traditional composite plates, shape memory alloy hybrid composite plates are
found to be able to reduce RMS values and prompt the evolution of vibration
about a buckled position and snap-through to vibration on the flat position.
